Boolean Algebra and Digital Logic
What the exam tests
Boolean Algebra and Digital Logic tests gates, truth tables, Boolean identities, De Morgan's theorems, simplification, and basic combinational and sequential circuits. You must simplify expressions and recognise gate behaviour.
Core rules
- Basic gates: AND (·), OR (+), NOT (′). NAND and NOR are universal gates; XOR gives 1 when inputs differ.
- Identities: A + 0 = A; A · 1 = A; A + A′ = 1; A · A′ = 0; A + AB = A; A + A′B = A + B.
- De Morgan: (A · B)′ = A′ + B′ and (A + B)′ = A′ · B′. Change the operator and invert each term.
- SOP is a sum of product terms; POS is a product of sum terms. A K-map groups 1s in powers of two (1, 2, 4, 8) to remove variables.
- A half adder outputs Sum = A ⊕ B and Carry = A · B; a full adder also accepts carry-in.
- A flip-flop stores one bit; it is sequential, while gates alone are combinational.
Worked example
Simplify F = A′B + AB + AB′. First group AB + AB′ = A(B + B′) = A. Then F = A′B + A. Use A + A′B = A + B, so F = A + B. Check with A = 0, B = 1: original A′B = 1, AB = 0, AB′ = 0, so F = 1; simplified A + B = 1. Check A = 1, B = 0: original 0 + 0 + 1 = 1; simplified 1. Correct.
Traps
Do not cancel terms that are not identical. De Morgan changes both the operator and each literal. In a K-map, groups must be rectangular and powers of two; wrapping around edges is allowed. XOR is not OR: 1 XOR 1 = 0. Do not call a flip-flop combinational.